Bregman circumcenters: monotonicity and forward weak convergence

Recently, we systematically studied the basic theory of Bregman circumcenters in another paper. In this work, aim to apply optimization algorithms. Here, propose forward monotonicity which is a generalization powerful Fejér and show weak convergence result monotone sequence. We also naturally introduce circumcenter mappings associated with finite set operators. Then provide sufficient conditions for sequence iterations mapping be monotone. Furthermore, prove that weakly converges point intersection fixed sets relevant operators, reduces known circumcentered method under Euclidean distance. addition, particular examples are provided illustrate isometry Browder’s demiclosedness principle, our result.